Exumple: Solue-the ditfereutial equation dy 2 dey

Q: 1. Calculate the moment of inertia about x-axis of the first quadrant portion of the curve: y = 4-…

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Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: at Solve thie équation use Eulers methoc- ds -t X-ツ dx x+y y(6)%=1

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Q: (х+ siny)dx+ (хcosy— 2y)dy 3D0

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Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A: 2∂z∂x=2xaa=xp, where p=∂z∂x2∂z∂y=2ybb=yq, where q=∂z∂y2z=x2xp+y2yq2z=px+qy

Q: correct to three decimal places by Trapezoidal rule with 1 +x dx Evaluate I= h=0-5.

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Q: Find a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: y = [cosh(2x)]ot*( 1 cot-1 3 Vx

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Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A: Given equation is 2z=x2a+y2b2p=2xa, where ∂z∂x=p and 2q=2yb, q=∂z∂ya=xp and b=yq2z=x2xp+y2yq2z=px+qy

Q: Q2\ Shoe that another from of Euler- * Lagrange equation is : L, -L,½ -y'L,ý - y"L,51 = 0 . - y 'Ly5…

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Q: dx 4.Exaluate I=| correct to three decimal places by Trapezoidal rule with h=0-25.

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Q: Q6/ Find the moment of inertia and radius of gyration about the x-axis of a thin plate bounded by…

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Q: Solve 3x – 6 ≥ 0 graphically intwo dimensional plane.

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Q: 28. Se cost sin 2t dt

A: ∫0πecostsin2tdtSolution :∫0πecostsin2tdt2∫0πecostsintcostdtlet, cost=x-sintdx=dxsintdx=-dxat…

Q: et secydx + sinydy = 0

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Q: Find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis

A: We have to find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis.

Q: Using figualve mme thod X + 2 dt 2. dy X - 29

A: To find the eigenvalues λ of the matrix A, solve the characteristic equation A-λI=0 for λ. To obtain…

Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: EXERCISE 1 dy -dx = 0

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Q: EXAM Q1-If x= cot-1 VE, y =,-. find dy d2y dx' dx2 at t = 2.

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Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

Q: 6- y" + 4y = cot(t)

A: Given:        y''+4y=cott        4yt+d2dt2yt=cott The differential has the form        y''+py'+qy=s…

Q: :Use variation of parameters to solve dx Зх — Зу + 4 dt dy 3D 2х — 2у — 1 dt

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Q: A-Estimate J, 2e-3* dx using trapezoidal rule with four subinterval round your answer to one decimal…

A: Given is the integral  ∫-11 2e-3xdx The aim is evaluate the integral using trapezoidal rule.

Q: whose x-coordinates are equally ine with parabolic runout conner

A: Given as.     python code :

Q: The projectile is thrown at the angle of 45 degrees with the initial velocity of 1 meter per second.…

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Q: Ex. 2. Prove thät if two equal and perfectly elastic balls moving in the same direction collide…

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Q: Solve (1+siny)dylx=[(2ycosy-(secy+tany)]dy.

A: This question is taken from a differential equation in which we have to solve the equation and take…

Q: 1 Evaluate dx by using Trapezoidal rule. Hence obtain 1 + x2 he approximate value of .

A: I am attaching image so that you understand each and every step.

Q: 2sin(y)cos(y) sint(y)+costy) dy

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Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: Find the Sufface arca 0f the soid of revolution Obtained bu rotatig y=+2x With TtxE2 around メーaxis、…

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Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

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Q: Describe the motion of a particle with posi- tion P(x, y) when x = 5 sin t, Y = 2 cost

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Q: s being pumped into a spherical ballo nge of the radius when the radius reac

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Q: dy Differentiate parametrically to find dx in terms of t: 1 y = 2t2 + 4 X = |

A: x = 1/(t-1) y = 2t2 + 4 We have to find dy/dx

Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: Integrate both sides dy = -dx

A: the given integral equation is                             ∫1y2dy=∫1xdx

Q: 2dy -2y 2. zt at

A: Solved below

Q: | sec? (y) /2+ tan(y) dy V

A: To evaluate: ∫0π sec2y 2+tan ydy

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

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Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: Determine the speed (in meters per second) of a particle with a trajectory (2 sin (3t), 9 cos (3t)),…

A: Consider the given parametric equation of the trajectory of the particle, 2sin3t,9cos3t so we can…

Q: Find dt y = 31(21? – 5) $ dy dt

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Q: Find the radius R, of curvature to the hyperbola y = x + 3x² – x³ at the point x = 0 given that R =…

A: To find the radius R, of curvature to the given hyperbola at point x = 0.

Q: Find the moment of inertia of the solid formec y2 = 2x and th

A: Introduction: If a solid is formed by revolving an area about the y-axis, then the moment of inertia…

Q: dy Find where y = sec-' (V3x³). dx

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Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.